利用冲突信息降维的进化高维目标优化算法

进化多目标优化算法求解高维目标优化问题面临收敛能力、计算复杂度、决策以及Pareto前沿的可视化等困难，其根本原因是目标空间维数高。目标降维通过丢弃冗余目标，为缓解高维目标优化求解困难提供一种新思路。本文提出利用冲突信息降维的分解进化高维目标优化算法（CIOR-MOEA/D）。该方法通过衡量目标在近似解集上体现的冲突性，构造问题的冲突信息矩阵，对该矩阵进行特征分析，确定目标的重要性程度，实现维数约简，并利用分解进化多目标优化算法（MOEA/D）对重要子目标集合进行分解进化,从而得到问题的近似解集。实验结果表明,本文提出的目标降维算法在降维的准确性与鲁棒性上均表现突出，能够有效地处理冗余高维目标优化问题。      

高维多目标优化中基于稀疏特征选择的目标降维方法

目标降维算法通过去除冗余的目标达到简化问题规模的目的,为求解高维多目标优化问题提供了一种新的思路和方法.近似解集的几何结构特征和Pareto占优关系从不同侧面反映了多目标优化问题的内在结构特性,而现有算法仅利用其中一种特征分析目标之间的关系,具有较大局限性.本文提出基于稀疏特征选择的目标降维方法,该方法利用近似解集的几何结构特征构建稀疏回归模型,求解高维目标空间映射为低维目标子空间的稀疏投影矩阵,依据此矩阵度量目标的重要性,并利用Pareto占优关系改变程度选择满足误差阈值的目标子集,实现目标降维.通过与其他已有目标降维算法比较,实验结果表明本文提出的降维算法具有较高的准确性,并且受近似解集质量的影响较小.     

基于均匀设计的多目标进化算法

现实生活中的很多决策问题都要考虑同时优化若干个目标,多目标优化算法就是要从所有可能的方案中找到最合理、最可靠的解决方案。如何在Pareto界面稀疏区域求得更多非劣解,则使所求出的解的分布更加均匀。如何求出距Pareto界面更近的非劣解以使所求出的解的质量更高。论文基于加权平均法和均匀设计方法设计了一种解决多目标优化问题的新算法。首先,为了找到在Pareto界面上尽可能多、且均匀分布的点,利用均匀设计方法设计了一个交叉算子,该算子让稀疏部分的相邻点进行均匀交叉,以使算法在稀疏部分能找到更多的非劣解,从而使其所求解分布更加均匀。其次,为了克服加权平均法不能找到Pareto界面非凸部分解的缺点,考虑到非劣解界面上相邻距离较远的一对点之间有可能是非劣解界面上非凸部分之一的情况,分别将此两点与距其最近的非劣解集外的点进行交叉,以期在该两点之间找到新的非劣解,这样可能在非劣解界面的非凸部分找到更多的解。最后对两个测试问题进行了数值试验,并和著名的NSGA-Ⅱ算法用算法性能评价的三种度量进行了比较,结果表明了本文算法是有效的。     

多目标量子编码遗传算法

如何使算法快速收敛到真正的Pareto前沿,并保持解集在前沿分布的均匀性是多目标优化算法重点研究解决的问题。该文提出一种基于量子遗传算法的多目标优化算法,利用量子遗传算法的高效全局搜索能力,在整个解空间内快速搜索多目标函数的Pareto最优解,利用量子遗传算法维持解集多样性的特点,使搜索到的Pareto最优解在前沿均匀分布。通过求解带约束的多目标函数优化问题,对该文算法的多目标优化性能进行了考察,并与NSGAII,PAES,MOPSO和Ray-Tai-Seows算法等知名多目标优化算法进行比较,结果证明了该文算法的有效性和先进性。     

非线性分类的分割超平面快速集成方法

直接营销策略的分割超平面(Separating HyperPlane,SHP)方法所构建的线性超平面(Linear HyperPlane,LHP)函数集的Vapnik-Chervonenkis(VC)维不超过9,并且能够快速分类和保护数据隐私,但其训练速度慢,对样本分布敏感以及不能解决非线性等问题。为此,该文提出一种适合大样本问题的非线性分类方法,称为分割超平面的快速集成方法(Fast Ensemble of Separating HyperPlane,FE-SHP)。此方法先将训练样本划分为多个集合并分别构造它们的次优线性超平面,然后利用径向基函数(Radical Basis Function,RBF)改善次优线性超平面的非线性能力,同时引进优化权提升次优线性超平面的非线性集成效果,并将集成输出转化为概率输出,进而通过梯度下降法最大化训练样本的交叉熵对数似然函数求解相关参数。UCI数据集的实验结果表明,FE-SHP在处理大样本方面具有较好的优势。     

一种基于粒子群算法的螺旋迭代模型研究

实际工程优化过程中,对于多个目标的优化与求解最优值是值得研究的一个问题。文章基于粒子群算法研究多目标优化问题,实现二维多目标搜索,运用粒子群多目标求解模型迭代实现动态多目标搜索,最终得到非劣解在目标空间中的分布,构成了Pareto面,得到非劣解集,在实际问题中,提供最优解的备选,为工程实践优化和筛选最优解问题提供参考依据。     

基于粒子群优化的地震应急物资多目标调度算法

合理高效地优化调度救灾物资对提升地震应急救援效果具有重要意义。地震应急需要同时兼顾时效性、公平性和经济性等相互冲突的多个调度目标。该文对地震应急物资调度问题建立了带约束的3目标优化模型，并设计了基于进化状态评估的自适应多目标粒子群优化算法(AMOPSO/ESE)来求解Pareto最优解集。然后根据“先粗后精”的决策行为模式提出了由兴趣最优解集和邻域最优解集构成的Pareto前沿来辅助决策过程。仿真表明该算法能有效地获得优化调度方案，与其他算法相比，所得Pareto解集在收敛性和多样性上具有性能优势。     

基于端元优化的非线性高光谱分解算法

针对高光谱图像中端元的可变性和光谱的非线性混合特性,提出一种基于端元优化的非线性光谱解混算法,通过加入阴影端元对混合像元的端元集进行优化,对优化的端元子集采用基于分层贝叶斯模型的双线性光谱分解算法进行光谱分解。模拟数据和真实数据实验表明,提出的算法能很好地解决高光谱图像中存在的阴影效应,分解效果优于FCLS和GBM算法。     

基于动态粒子群算法的多总线测试任务调度方法

测试任务调度多考虑资源约束和任务优先级约束, 在对消息实时性要求较高的航空总线测试设备中, 需要将任务调度的实时性能作为关键衡量指标。将剩余可调度时间和总线负载均衡程度作为优化目标, 在满足资源限制的前提下结合总线协议特征, 提出一种包含精英集的动态粒子群算法进行多目标优化, 得到Pareto前沿和非劣解集, 并从中选择非劣解作为测试消息队列。实验仿真证明了该调度方法的有效性, 且测试消息队列能够满足高实时性要求, 并平衡总线间负载。     

一种求解多目标优化问题的粒子群算法的研究

为改善多目标粒子群算法的收敛性和多样性,通过对粒子群算法全局极值和个体极值选取方式的研究,采用随机选取和评估选取相结合的方法选取全局极值和个体极值,提出了一种可用于解决多目标优化问题的粒子群优化算法,从而实现了对多目标优化问题的非劣最优解集的搜索,仿真实验结果证明算法是有效的。     

高维多目标优化问题融入决策者偏好的集合进化优化方法

高维多目标优化问题普遍存在且非常重要,但是,已有的解决方法却很少.本文提出一种有效解决该问题的融入决策者偏好的集合进化优化方法,该方法首先基于决策者给出的每个目标的偏好区域,将原优化问题的目标函数转化为期望函数;然后,以原优化问题的多个解形成的集合为新的决策变量,以超体积和决策者期望满足度为新的目标函数,将优化问题转化为2目标优化问题;最后,采用多目标集合进化优化方法求解,得到满足决策者偏好且收敛性和分布性均衡的Pareto优化解集.将所提方法应用于4个基准高维多目标优化问题,并与其他2种方法比较,实验结果验证了所提方法的优越性.     

基于自适应支配准则的高维多目标进化算法

基于松弛支配的高维多目标进化算法（Many-objective Evolutionary Algorithms,MaOEAs）由于能够有效地提高区分解的能力,受到广泛关注,但该类大多数算法处理不同目标的优化问题时普适性较差.针对这个问题,本文提出一种基于自适应支配准则的高维多目标进化算法（Adaptive Dominance Criterion Based Evolutionary Algorithm for Many-objective Optimization,ADCEA）.首先,自适应准则（Adaptive Dominance Criterion,ADC）根据目标空间中相邻解间的角度信息和目标数目,设计一种自适应小生境方法,并结合收敛性指标信息,实现对候选解的非支配排序.然后,为了进一步增强种群的多样性,在环境选择中引入参考向量分割种群技术;最后,构建合理的适应度函数,并根据适应度值大小选取收敛性和多样性较好的非支配解集.实验证明,本文所提的方法在处理不同目标的优化问题时普适性提高,并在平衡种群的收敛性和多样性上取得显著效果.     

An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme

In this paper, a special nonlinear bilevel programming problem (nonlinear BLPP) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first construct a specific optimization problem with two objectives. By solving the specific problem, we can decrease the leader's objective value, identify the quality of any feasible solution from infeasible solutions and the quality of two feasible solutions for the equivalent single objective optimization problem, force the infeasible solutions moving toward the feasible region, and improve the feasible solutions gradually. We then propose a new constraint-handling scheme and a specific-design crossover operator. The new constraint-handling scheme can make the individuals satisfy all linear constraints exactly and the nonlinear constraints approximately. The crossover operator can generate high quality potential offspring. Based on the constraint-handling scheme and the crossover operator, we propose a new evolutionary algorithm and prove its global convergence. A distinguishing feature of the algorithm is that it can be used to handle nonlinear BLPPs with nondifferentiable leader's objective functions. Finally, simulations on 31 benchmark problems, 12 of which have nondifferentiable leader's objective functions, are made and the results demonstrate the effectiveness of the proposed algorithm.     

A binary adaptive decision-selection equalizer for channels with nonlinear intersymbol interference

An enhanced adaptive decision feedback equalizer (ADFE) is presented for binary data transmission applications where the communication channel exhibits nonlinear intersymbol interference (ISI). The nonlinearity in the channel manifests itself as a distorted constellation space constructed from the equalizer input state variables. Since a conventional ADFE can construct a hyperplane decision boundary of only one orientation with symmetrically spaced distance from the origin as a function of the detected feedback symbols and feedback filter coefficient values, there is room for improvement since the distorted constellation of the nonlinear system is better served by hyperplane boundaries of varying orientation. The method proposed here is not to feed back the decision variables but, instead, to use these binary variables to choose and adapt different sets of coefficients, i.e., different hyperplane boundaries. Hence, the name given to this new method is the adaptive decision-selection equalizer (ADSE). Although the hyperplane may not be the optimum boundary for the conditional constellations, in many cases, it is an adequate approximation. Nonetheless, for nonlinear channels, the ADSE is generally an improvement over the conventional ADFE in high signal-to-noise ratio (SNR) regimes, where the bit error rate (BER) is within the desired operating range. The major advantage of the new method is improved performance on the studied channel while retaining simplicity when implemented as a variation of the least-mean-squared (LMS) algorithm. Some drawbacks are decreased convergence rate and limitations of the minimum mean-squared-error (MMSE) strategy of optimization, as implemented by the LMS algorithm, for a system where error probability, not MMSE, is important.     

Parameters optimization for cooperative sensing in multi‐channel cognitive radio networks

In this paper, we propose a relatively complete and robust optimization model under the scenario where multisecondary users cooperatively sense multi‐channels. The objective of this model is to maximize the system throughput, meanwhile aims to jointly optimize the parameters including the sensing time and the weight coefficients of the sampling results. Because this model is a nonlinear optimization model, we instead adopt a heuristic sequential parameters optimization method (SPO) to solve the model. The method begins with deriving the lower bound of the objective function of the optimization model. Then, it maximizes this lower bound by optimizing the weight coefficients through solving a series of suboptimal problems using Lagrange method. Given that the weight coefficients are found, it finally transforms the problem into another monotonic programming problem and exploits a fast‐convergent polyblock algorithm to find an optimized sensing time parameter. We finally conduct extensive experiments by simulations. The results demonstrate that, in terms of the throughput gained by the system, SPO can deliver a solution that is up to 99.3% of the optimal on average, which indicates that SPO can solve the proposed optimization model effectively. In addition, we also show the performance advantage of the proposed model on improving the system throughput by comparing with other state‐of‐the‐art optimization models. Wireless Communications and Mobile Computing. Copyright © 2012 John Wiley & Sons, Ltd.     

Minimum class variance support vector machines.

In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher's discriminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis (PCA). Afterward, the MCVSVMs are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary Hilbert spaces defined by Mercer's kernels. In that case, it is shown that, under kernel PCA, the nonlinear optimization problem is transformed into an equivalent linear MCVSVMs problem. The effectiveness of the proposed approach is demonstrated by comparing it with the standard SVMs and other classifiers, like kernel Fisher discriminant analysis in facial image characterization problems like gender determination, eyeglass, and neutral facial expression detection.     

A self learned invasive weed-mixed biogeography based optimization algorithm for RFID network planning

The optimal placement of the RFID readers inaugurates an ongoing research field, namely the RFID network planning (RNP). The main issue in the RNP is to know how many readers have to be used and what is their best distribution that guarantees fulfillment of multiple objectives. The common RNP objectives are the optimal coverage, readers’ interference avoidance, redundant reader elimination, load balance among deployed readers and minimum power losses, which are considered as conflicting objectives that leads the RNP to be an NP-hard problem need to be solved. The contributions in this paper are: firstly, utilizing both the Biogeography based optimization (BBO) and the Hybrid Invasive Weed-Biogeography based optimization (HIW-BBO) as new algorithms have not used before for solving the RNP. Secondly, we proposed a Self Learning (SL) strategy with a mixed BBO Migration (MBBOM) operation to modify the HIW-BBO algorithm in an algorithm called Self Learned Invasive Weed-Mixed Biogeography based optimization (SLIWMBBO). Thirdly, the performance of the proposed SLIWMBBO algorithm is compared to both the HIW-BBO and the Self Adaptive Cuckoo Search (SACS) optimization algorithms according to a set of 13 benchmark functions. The results of this comparison encourage the application of the SLIWMBBO as an optimization algorithm for solving the complex problems. Lastly, the BBO, HIW-BBO and SLIWMBBO optimization algorithms are used for solving three complex RNP instances and compared to the SACS algorithm. Simulation results of the SLIWMBBO are outstanding and demonstrate its superiority over the compared algorithms.

     

Newton's method for nonparallel plane proximal classifier with unity norm hyperplanes

In our previous research we observed that the nonparallel plane proximal classifier (NPPC) obtained by minimizing two related regularized quadratic optimization problems performs equally with that of other support vector machine classifiers but with a very lower computational cost. NPPC classifies binary patterns by the proximity of it to one of the two nonparallel hyperplanes. Thus to calculate the distance of a pattern from any hyperplane we need the Euclidean norm of the normal vector of the hyperplane. Alternatively, this should be equal to unity. But in the formulation of NPPC these equality constraints were not considered. Without these constraints the solutions of the objective functions do not guarantee to satisfy the constraints. In this work we have reformulated NPPC by considering those equality constraints and solved it by Newton's method and the solution is updated by solving a system of linear equations by conjugate gradient method. The performance of the reformulated NPPC is verified experimentally on several bench mark and synthetic data sets for both linear and nonlinear classifiers. Apart from the technical improvement of adding those constraints in the NPPC formulation, the results indicate enhanced computational efficiency of nonlinear NPPC on large data sets with the proposed NPPC framework.